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Cubic threefolds and abelian varieties of dimension five
Author(s):
Sebastian
Casalaina-Martin;
Robert
Friedman
Journal:
J. Algebraic Geom.
14
(2005),
295-326.
Posted:
August 11, 2004
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
This paper proves the following converse to a theorem of Mumford: Let  be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point is three. Then  is isomorphic as a principally polarized abelian variety to the intermediate Jacobian of a smooth cubic threefold. The method of proof is to analyze the possible singularities of the theta divisor of  , and ultimately to show that  is the Prym variety of a possibly singular plane quintic.
References:
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Additional Information:
Sebastian
Casalaina-Martin
Affiliation:
Department of Mathematics, Columbia University, New York, New York 10027
Address at time of publication:
Department of Mathematics, SUNY Stony Brook, Stony Brook, New York 11794-3651
Email:
casa@math.columbia.edu, casa@math.sunysb.edu
Robert
Friedman
Affiliation:
Department of Mathematics, Columbia University, New York, New York 10027
Email:
rf@math.columbia.edu
PII:
S 1056-3911(04)00379-0
Received by editor(s):
July 28, 2003
Posted:
August 11, 2004
Additional Notes:
The first author was supported in part by a VIGRE fellowship from NSF Grant \#DMS-98-10750. The second author was supported in part by NSF Grant \#DMS-02-00810.
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